Ratio & Proportion Calculator

Ratios and proportions are among the most versatile mathematical tools you encounter in daily life. From resizing digital screen resolutions and scaling culinary recipes to reading map distances and mixing chemical solutions, understanding proportional relationships keeps everything in balance.

What Is the Difference Between a Ratio and a Proportion?

How to Solve for an Unknown Variable (Cross-Multiplication)

When one value in a proportion is unknown (e.g., /B = C/x$), you can solve for it in three steps using cross-multiplication:

1. Multiply the two numbers that are diagonal from each other ( imes C$).
2. Set that product equal to the remaining diagonal ( imes x$).
3. Divide both sides by the known diagonal value ( = (B imes C) / A$).

Example: If a car travels 150 miles on 5 gallons of gasoline, how many gallons are needed for 450 miles? Setting up $150 / 5 = 450 / x$ yields $150x = 2,250$, so = 15$ gallons.

Simplifying Ratios to Lowest Terms

Just like fractions, ratios can often be simplified into smaller whole numbers by dividing each term by their Greatest Common Divisor (GCD). For example, a screen resolution ratio of $1920 : 1080$ shares a GCD of 120; dividing both sides by 120 simplifies the ratio to the classic $16 : 9$ widescreen aspect ratio.

Dividing a Quantity into Proportional Parts

When dividing profits or physical resources according to a ratio like $2 : 3 : 5$ for a total pool of $1,000:

• Add the individual parts together: $2 + 3 + 5 = 10$ total shares.
• Find the value of one share: $$1,000 / 10 = $100$.
• Distribute the shares: Part 1 gets $$200$ ($2 imes $100$), Part 2 gets $$300$ ($3 imes $100$), and Part 3 gets $$500$ ($5 imes $100$).